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There are 7 consecutive integers and 6 consecutive integers. The average of the 7 integers is 3 less than the average of the 6 integers. The sum of the 6 integers is 6 more than the sum of the 7 integers. Find the average of the 7 integers.

1. 7
2. 8
3. 12
4. 10

Correct answer: 12

Solution

Let the average of the 7 integers be \(x\); then the average of the 6 integers is \(x+3\). Since sum of 6 integers is 6 more than sum of 7 integers, \(6(x+3)=7x+6\), giving \(x=12\).

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